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Question

The total no. of permutations of n(n>1) different things have taken not more than r at a time, when each thing may be repeated any number of times is?


A

nnr-1n-1

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B

nr-1(n-1)

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C

n(rn-1)(n-1)

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D

n(n-r)(n-1)

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Solution

The correct option is A

nnr-1n-1


Explanation of the correct option:

Total number of things are n.

If we take 1 thing at a time, then number of ways=n

If we take 2 thing at a time, then number of ways=n2

If we take 3 thing at a time, then number of ways=n3

So, for r number of things, number of ways =nr

Therefore total number of ways from 1 to r at a time is given by,

n+n2+n3+...........+nr=n(nr-1+nr-2+....+1)=n(nr-1+nr-2+....+1)(n-1)(n-1)=nnr-1n-1

Therefore, total number of ways is nnr-1n-1.

Hence option (A) is the correct option.


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